Zawartość
Pełne teksty:
Warianty tytułu
Abstrakty
CONTENTS
1. Introduction...................... 5
2. Definitions........................... 6
3. Stochastic processes.................. 7
4. Processes with independent increments...... 8
5. Sequential estimation for the Poisson process..... 12
6. Other processes with independent increments.......... 33
7. Efficiency for a given value of the parameter......... 39
8. Final remarks........................................... 43
References................................................ 45
1. Introduction...................... 5
2. Definitions........................... 6
3. Stochastic processes.................. 7
4. Processes with independent increments...... 8
5. Sequential estimation for the Poisson process..... 12
6. Other processes with independent increments.......... 33
7. Efficiency for a given value of the parameter......... 39
8. Final remarks........................................... 43
References................................................ 45
Słowa kluczowe
Tematy
Miejsce publikacji
Warszawa
Copyright
Seria
Rozprawy Matematyczne
tom/nr w serii:
60
Liczba stron
47
Liczba rozdzia³ów
Opis fizyczny
Dissertationes Mathematicae, Tom 60
Daty
wydano
1968
Twórcy
autor
- Politechnika Wrocławska, Katedra Matematyki, Department of Mathematics, Technical University, Wrocław
Bibliografia
- [1] R. R. Bahadur, Sufficiency and statistical decision functions, Ann. Math. Stat. 25 (1954), pp. 423-462.
- [2] D. Blackwell, Conditional expectation and unbiased sequential estimation, Ann. Math. Stat. 18 (1947), pp. 105-110.
- [3] R. H. Cameron and W. T. Martin, Transformation of Wiener integrals under translations, Ann. of Math. 45 (1944), pp. 386-396.
- [4] Transformation of Wiener integrals under a general class of linear
- transformations, Trans. Amer. Math. Soc. 58 (1945), pp. 184-219.
- [5] K. L. Chung, Foundations of the theory of continuous parameter Marlcov chains, Preceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability, vol. II, pp. 29-40.
- [6] D. A. Darling and A. F. J. Siegert, The first passage problem for a continuous Markov process, Ann. Math. Stat. 24 (1953), pp. 624-639.
- [7] J. L. Doob, Stochastic processes, New York 1953.
- [8] E. B. Dynkin (E. Б. Дынкин), Марковские процессы, Москва 1963.
- [9] A. Dworetzky, J. Kiefer and J. Wolfowitz, Sequential decision problems for processes with continuous time parameter. Testing hypotheses, Ann. Math. Stat. 24 (1953), pp. 254-264.
- [10] A. Dworetzky, J. Kiefer and J. Wolfowitz, Sequential decision problems for processes with continuous time parameter. Problems of estimation, Ann. Math. Stat. 24 (1953), pp. 403-415.
- [11] W. Feller, An introduction to probability theory and its applications, New York 1950.
- [12] R. Fortet, Les fonctions aletoires du type de Markoff associées a certaines équations linéaires aux dérivées partielles du type parabolique, Journ. Math. Pures Appl. 22 (1943), pp. 177-243.
- [13] I. M. Gelfand, A. M. Jaglom (И. M. Гельфанд, A. M. Яглом), Интегрирование в функциональных пространствах и его применения в квантовой физике, Усп. Мат. Наук 11 (1) (1956), рр. 77-114.
- [14] М. A. Girschick, F. Mosteller and L. J. Savage, Unbiased estimates for certain binomial sampling problems with applications, Ann. Math. Stat. 17 (1946), pp. 13-23.
- [15] J. S. Gradsztein, J. M. Ryzik (И. С. Градштейн, И. M. Рыжик), Таблицы интегралов, сумм, рядов и произведений, Москва 1963.
- [16] U. Grenander, Stochastic processes and statistical inference, Ark. Mat. 1 (1950), pp. 195-277.
- [17] M. H. De Groot, Unbiased sequential estimation for binomial populations, Ann. Math. Stat. 30 (1959), pp. 80-101.
- [18] P. R. Halmos and L. J. Savage, Application of the Radon Nikodym theorem to the theory of sufficient statistics, Ann. Math. Stat. 20 (1949), pp. 225-241.
- [19] G. A. Hunt, Some theorems concerning Brownian motion, Trans. Amer. Math. Soc. 81 (1956), pp. 294-309.
- [20] K. Ito (К. Ито), Вероятностные процессы, выпуск I, Москва 1963.
- [21] A. N. Kolmogoroff (A. H. Колмогоров), Основные понятия теории вероятностей, Москва 1936.
- [22] Е. L. Lehmann and С. Stein, Completeness in sequential case, Ann. Math. Stat. 21 (1950), pp. 376-385.
- [23] A. W. Skoroehod (А. В. Скороход), О дифференцируемости мер, соответствующих случайным процессам. I. Процессы с независимыми приращениями. Теория вероятностей и её применения, Москва 1957 (рр. 417-443).
- [24] A. Wald, Sequential analysis, New York 1952.
- [25] J. Wolfowitz, On sequential binomial estimation, Ann. Math. Stat. 17 (1946), pp. 489-493.
- [26] J. Wolfowitz, The efficiency of sequential estimations and Wald's equation for sequential processes, Ann. Math. Stat. 18 (1947), pp. 215-230.
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